Accidentally Erased my Mac Mini Firmware Lock Activated, Apple Does not Consider this popular Auction Website Transactions as Valid?

The firmware lock does not stop you usingr a Mac but it prevents it being started up from anything other than the internal disk without the password. Evidently the vendor set this lock. You didn't notice it until you erased the disk: now you can only proceed by starting from an installer volume, which the lock prevents you from doing.

Your beef is with the vendor who should not have sold you a locked device. Since he set the lock (there is no likelihood of it being some sort of electical glitch) he should (in theory) know the password and should provide you with it.

If he can't or won't do this you have a case for demanding a refund. However using an auction site makes this difficult: it would depend on the policy of the auction site and they may well not accept responsibility.

As with Activation Lock I would expect Apple not to unlock a device other than for the original owner and then only with full purchase documentation. Their reaction to you would tend to confirm this. In general Apple won't get involved with second-hand devices other than a straightforward paid-for repair.

Your first step is, if possible, to contact the vendor and demand either the password or your money back. Failing that you should approach the auction site and enquire about their policy in cases like this.

And by the way, how did you manage to erase the disk? You can't erase the disk you are running from, and if there is a firmware lock you can't start up from anything else - so you can't erase the disk.

Are you sure it's firmware lock and not Activation Lock? - though even if it is the advice comes to the same thing.